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Step #1 ...

sudo apt-get -y update;

sudo apt-get -y upgrade;

sudo apt-get -y dist-upgrade;

sudo apt-get -y clean;

sudo apt-get -y autoremove;

... results in ...

Hit:1 https://download.sublimetext.com apt/stable/ InRelease

Hit:2 http://linux.teamviewer.com/deb stable InRelease                                                                                                 

Hit:3 http://archive.canonical.com/ubuntu bionic InRelease                                                                                             

Ign:4 http://dl.google.com/linux/chrome/deb stable InRelease                                                                                           

Hit:5 http://dl.google.com/linux/chrome/deb stable Release                      

Hit:7 http://mirror.clibre.uqam.ca/ubuntu bionic InRelease

Hit:8 http://mirror.clibre.uqam.ca/ubuntu bionic-updates InRelease

Hit:9 http://mirror.clibre.uqam.ca/ubuntu bionic-backports InRelease

Hit:10 http://mirror.clibre.uqam.ca/ubuntu bionic-security InRelease

Reading package lists... Done 

Reading package lists... Done

Building dependency tree       

Reading state information... Done

Calculating upgrade... Done

0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

Reading package lists... Done

Building dependency tree       

Reading state information... Done

Calculating upgrade... Done

0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

Reading package lists... Done

Building dependency tree       

Reading state information... Done

0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

Step #2 ...

sudo apt install libnotify-dev

... results in ...

Reading package lists... Done

Building dependency tree       

Reading state information... Done

Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming.

The following information may help resolve the situation:



The following packages have unmet dependencies:

 libnotify-dev : Depends: libglib2.0-dev (>= 2.26) but it is not going to be installed

                 Depends: libgdk-pixbuf2.0-dev but it is not going to be installed

E: Unable to correct problems, you have held broken packages.

Step #3 ...

sudo aptitude install libnotify-dev

... results in ...

The following NEW packages will be installed:

  gcc-8-base:i386{ab} libblkid1:i386{ab} libc6:i386{a} libelf1:i386{a} libffi6:i386{a} libgcc1:i386{ab} libgdk-pixbuf2.0-dev{a} 

  libglib2.0-0:i386{ab} libglib2.0-bin:i386{ab} libglib2.0-dev{ab} libglib2.0-dev-bin{a} libmount1:i386{ab} libnotify-dev libpcre16-3{a} 

  libpcre3:i386{a} libpcre3-dev{a} libpcre32-3{a} libpcrecpp0v5{a} libpng-dev{a} libpng-tools{a} libpthread-stubs0-dev{a} libselinux1:i386{a} 

  libuuid1:i386{ab} libx11-dev{ab} libx11-doc{a} libxau-dev{a} libxcb1-dev{a} libxdmcp-dev{a} pkg-config{a} x11proto-core-dev{a} x11proto-dev{a} 

  xorg-sgml-doctools{a} xtrans-dev{a} zlib1g:i386{a} zlib1g-dev{a} 

0 packages upgraded, 35 newly installed, 0 to remove and 0 not upgraded.

Need to get 10.6 MB of archives. After unpacking 48.7 MB will be used.

The following packages have unmet dependencies:

 libmount1 : Breaks: libmount1:i386 (!= 2.31.1-0.4ubuntu3.2) but 2.31.1-0.4ubuntu3.1 is to be installed

 libmount1:i386 : Breaks: libmount1 (!= 2.31.1-0.4ubuntu3.1) but 2.31.1-0.4ubuntu3.2 is installed

 gcc-8-base : Breaks: gcc-8-base:i386 (!= 8.2.0-1ubuntu2~18.04) but 8-20180414-1ubuntu2 is to be installed

 gcc-8-base:i386 : Breaks: gcc-8-base (!= 8-20180414-1ubuntu2) but 8.2.0-1ubuntu2~18.04 is installed

 libgcc1 : Breaks: libgcc1:i386 (!= 1:8.2.0-1ubuntu2~18.04) but 1:8-20180414-1ubuntu2 is to be installed

 libgcc1:i386 : Breaks: libgcc1 (!= 1:8-20180414-1ubuntu2) but 1:8.2.0-1ubuntu2~18.04 is installed

 libblkid1 : Breaks: libblkid1:i386 (!= 2.31.1-0.4ubuntu3.2) but 2.31.1-0.4ubuntu3.1 is to be installed

 libblkid1:i386 : Breaks: libblkid1 (!= 2.31.1-0.4ubuntu3.1) but 2.31.1-0.4ubuntu3.2 is installed

 libuuid1 : Breaks: libuuid1:i386 (!= 2.31.1-0.4ubuntu3.2) but 2.31.1-0.4ubuntu3.1 is to be installed

 libuuid1:i386 : Breaks: libuuid1 (!= 2.31.1-0.4ubuntu3.1) but 2.31.1-0.4ubuntu3.2 is installed

 libglib2.0-bin : Conflicts: libglib2.0-bin:i386 but 2.56.1-2ubuntu1 is to be installed

 libglib2.0-bin:i386 : Conflicts: libglib2.0-bin but 2.56.3-0ubuntu0.18.04.1 is installed

 libglib2.0-dev : Depends: libglib2.0-0 (= 2.56.1-2ubuntu1) but 2.56.3-0ubuntu0.18.04.1 is installed

 libx11-dev : Depends: libx11-6 (= 2:1.6.4-3) but 2:1.6.4-3ubuntu0.1 is installed

 libglib2.0-0 : Breaks: libglib2.0-0:i386 (!= 2.56.3-0ubuntu0.18.04.1) but 2.56.1-2ubuntu1 is to be installed

 libglib2.0-0:i386 : Breaks: libglib2.0-0 (!= 2.56.1-2ubuntu1) but 2.56.3-0ubuntu0.18.04.1 is installed

open: 44; closed: 1251; defer: 26; conflict: 34                                                                                                        



The following actions will resolve these dependencies:



      Keep the following packages at their current version:

1)      gcc-8-base:i386 [Not Installed]                    

2)      libblkid1:i386 [Not Installed]                     

3)      libc6:i386 [Not Installed]                         

4)      libelf1:i386 [Not Installed]                       

5)      libffi6:i386 [Not Installed]                       

6)      libgcc1:i386 [Not Installed]                       

7)      libgdk-pixbuf2.0-dev [Not Installed]               

8)      libglib2.0-0:i386 [Not Installed]                  

9)      libglib2.0-bin:i386 [Not Installed]                

10)     libglib2.0-dev [Not Installed]                     

11)     libmount1:i386 [Not Installed]                     

12)     libnotify-dev [Not Installed]                      

13)     libpcre3:i386 [Not Installed]                      

14)     libselinux1:i386 [Not Installed]                   

15)     libuuid1:i386 [Not Installed]                      

16)     libx11-dev [Not Installed]                         

17)     zlib1g:i386 [Not Installed]                        







Accept this solution? [Y/n/q/?] y

... but accepting merely gets me ...

No packages will be installed, upgraded, or removed.

0 packages upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

Need to get 0 B of archives. After unpacking 0 B will be used.

Versions:

lsb_release -a

... shows ...

No LSB modules are available.

Distributor ID: Ubuntu

Description:    Ubuntu 18.04.1 LTS

Release:    18.04

Codename:   bionic

How can I resolve this and get the package to install?

Update 2019-03-28 18:05 EST

Also tried ...

sudo apt install libglib2.0-dev libgdk-pixbuf2.0-dev

... getting ...

 libgdk-pixbuf2.0-dev : Depends: libx11-dev but it is not going to be installed

 libglib2.0-dev :       Depends: libglib2.0-0 (= 2.56.1-2ubuntu1) but 2.56.3-0ubuntu0.18.04.1 is to be installed

                        Depends: libglib2.0-bin (= 2.56.1-2ubuntu1)

Update 2019-03-29 06:45 EST

Per the question by @fkraiem:

apt-cache policy libglib2.0-dev

... produces ...

libglib2.0-dev:

  Installed: (none)

  Candidate: 2.56.1-2ubuntu1

  Version table:

     2.56.1-2ubuntu1 500

        500 http://mirror.clibre.uqam.ca/ubuntu bionic/main amd64 Packages

Per the concern expressed by @Mamayogi:

dpkg --print-architecture; dpkg --print-foreign-architectures;

... produces ...

amd64

i386

... but, nevertheless, the command sudo apt install libnotify-dev gives the same 'unmet dependencies' result as at first.

One possible cause of unavailable dependencies, especially when the desired package is an official one, is an out-of-date archive mirror, as was the case here. One can see a list of all available archive mirrors and their update status here; if your mirror is out of date, try another one.